I played AD&D as a kid. Was curious about getting into a play by post game of pathfinder or 4.0. I see lots of game ads but I can't seem to find the actual games. I would really like to read some ongoing campaigns before I commit to joining a game. Are the game threads hidden from non-players or am I just not looking in the right place?

welcome in bud!
if you scroll down to the bottom of the game ads page, you can select the system and settings for a search, also, when looking in an ad, at the top of the ad page you can click a link for that games forums.
I hope this helps a bit.

Even without being a reader you can read a lot of most games, except posts and threads marked Private. Check the archives of a particular game forum. Follow the directions given by Yohan and sample some games of the systems you are interested in. If you like one, apply to the game as a reader or send a PM to the DM to ask for the permission.

You have to be a member of the game to read the threads. You can apply to be a "reader" to the GM, which will give you read only access.

Ignore tats, it's completely wrong.

The only stuff that's hidden as bzipser said are threads explicitly made private by the GM or smoe section of text within a post which has private tags. The private features are used to varying degrees by different GMs but the vast majority of threads in most games aren't private. You don't need to become a reader to get a good idea of how everything works but it will allow you to see everything the GM sees.

There's a stickied thread at the top of general discussion with some examples of how things work. They might be a good place to start.

There are 2 places you can land in a game when following a link depending on type, these are:
The game profile which will show members, adverts and other metadata.
The game forums - this should show the most active threads (but is dependant on how the GM has organized things so could show no threads). Down the left side there may be threadgroups and wiki pages. Click threadgroups to show the threads in that group.

If the game is archived all private settings are removed and the game does not have it's own forum. Therefore you can view everything but threads are not as well organised. From the game profile of an archived game there's a link to the top left marked "archived threads" which will display a list of all threads.
There is one other type of private I haven't mentioned, private games, but you can't see any sign of those anyway so I won't cover them.